• Journal for History of Mathematics
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• v.18 no.3
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• pp.107-117
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• 2005

In this paper, we introduce linear approximate Henstock integral equations that is slightly different from linear Henstock integral equations, and we also offer an example which shows that some integral equation has a solution in the sense of the approximate Henstock integral but does not have any solutions in the sense of the Henstock integral. Furthermore, we investigate the existence and uniqueness of solution of the approximate Henstock integral equation.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.709-717
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• 2005

Integral equations occur naturally in many fields of mechanics and mathematical physics. We consider the Fredholm integral equation of the first kind.In this paper we are interested in integral equation of convolution type. We give approximate solution by Meyer wavelets

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.22 no.7
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• pp.468-473
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• 2010

This paper deals with approximate integral solutions to the one-dimensional model describing the charging process of stratified thermal storage tanks. Temperature is assumed to be the form of Fermi-Dirac distribution function, which can be separated to two sets of cubic polynomials for each hot and cold side of thermal boundary layers. Proposed approximate integral solutions are compared to the previous works of the approximate analytic solutions and show reasonable agreement. The approach, however, has benefits in mathematical difficulties, complicated solution form and unstable convergence of series solution founded in the previous analytic solutions. Solutions for a semi-infinite region, which have simple closed form solutions, give close agreement to those for a finite region. Thermocline thickness is obtained in closed form and shows proportional behavior to the square root of time and inverse proportional behavior to the square root of flow rate.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.699-721
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• 2015

This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.83-92
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• 2021

This paper studies approximate solutions for a class of nonlinear diffusion population models. Our methods are to use the fundamental solution of heat equations to construct integral forms of the models and the well-known Banach compression map theorem to prove the existence of positive solutions of integral equations. Non-steady-state local approximate solutions for suitable harvest functions are obtained by utilizing the approximation theorem of multivariate continuous functions.

• Journal of Advanced Marine Engineering and Technology
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• v.29 no.5
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• pp.509-518
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• 2005

Liquid film thickness in laminar film condensation for flow over a flat plate generally is so thin that both fluid acceleration and thermal convection within the liquid film can be neglected. An integral solution method is proposed to solve the conjugate problems of laminar film condensation and heat conduction in a solid wall. It is found that approximate solutions of the governing equations involve four physical parameters to describe the conjugate heat transfer problem for laminar film condensation. It is shown that the effects of interfacial shear. mass transfer and local heat transfer are strongly dependent on the thermo-physical properties of the working fluids and the Jacob number.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.657-667
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• 2001

We propose a statistical interpolation approximate solution for a nonlinear stochastic integral equation of a stock price process. The proposed method has the order O(h$^2$) of local error under the weaker conditions of $\mu$ and $\sigma$ than those of Milstein' scheme.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.211-223
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• 2012

This paper deals with large deformation post-buckling of a linear-elastic and hygrothermal beam with axially nonmovable pinned-pinned ends and subjected to a significant increase in swelling by an alternative method. Analytical approximate solutions for the geometrically nonlinear problem are presented. The solution for the limiting case of a string is also obtained. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation, and supplementary condition with cosinoidal nonlinearity can also be simplified to be a polynomial integral equation. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. Two approximate formulae for load along axis, potential strain for free hygrothermal expansion and periodic solution are established for small as well as large angle of rotation at the end of the beam. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.8
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• pp.765-774
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• 2004

In this paper, a novel approximate solution for scattering by a very thin planar homogeneous dielectric scatterer with an arbitrary shape is formulated. This solution is based on a volumetric integral equation and is expressed in terms of Fourier transform. It is shown that the obtained solution is reduced to an exact solution for an infinite dielectric slab. For 2D, or 3D scatterers, the formulation is verified numerically. Especially fur edge-on TM polarized wave incidence a closed-form solution of backscattering from a thin dielectric half-plane is formulated, which is very accurate for wide range of normalized surface impedance except very low impedances(│η│〈0.5).

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.3 no.4
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• pp.215-221
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• 1991

Laminar film condensation of a saturated vapor in forced flow over a flat plate is analyzed by using integral method. Laminar condensate film is so thin that the inertia and thermal convection terms in liquid flow can be neglected. Approximate solutions for water are presented and well agreed with the similarity solutions over the wide range of physical parameter, Cp1(Ts-Tw)/Pr.hfg. For the strong condensation case, it is found that magnitude of the interfacial shear stress at the liquid-vapor interphase boundary is approximately equal to the momentum transferred by condensation, i.e., ${\tau}_i{\simeq}\dot{m}(U_O-U_i)$.